A statement on the club website said on Monday: "While thanking Mancini and his staff for the successes obtained in four seasons at the helm, Inter have the great pleasure of welcoming Mourinho and his assistants and wishing them all the best."
The 45-year old coach will work alongside Rui Farias, Silvino and Andrei Villas Boas. The assistant coach will be Giuseppe Baresi.
According to Football Italia, Mourinho signed a three-year contract and will earn around £7m per year to become the highest paid coach in history of the Serie A.
The former Chelsea manager, who won two Premier League titles, has been linked with Inter job since last March as Mancini has been under fire by the fans.
The former Italy striker lived some tense moments in the backroom and President Massimo Moratti decided to sack him despite winning a third straight Scudetto title for the Nerrazzuri.
Mourinho will be presented on Tuesday morning at a press conference.